Phase behavior of a family of continuous two-dimensional $n$-vector models with $n=2$, 3, and 4

In this work we investigate the phase behavior of a family of continuous bidimensional $n$-vector models (with $n=2$, 3, and 4) using Monte Carlo simulation. In all cases we detect the presence of a defect mediated order-disorder transition of the Berezinskii-Kosterlitz-Thouless type with critical temperatures that decrease with the spin dimensionality. Coupled with the order-disorder transition a gas-liquid equilibrium is found at low temperatures. Here one observes that the stability region of the liquid phase shrinks with the growing spin dimensionality, in parallel with a decrease in magnitude of the angular averaged spin-spin interaction.

Figure 1

(Color online) Angular average of the low density limit of the potential of mean force for coplanar $\mathbb{R}{P}^{n-1}$ spins.

Figure 2

(Color online) Reduced excess constant volume specific heat per particle in units of $k_B$ [Eq. (30)] and susceptibility [Eq. (20)] for the coplanar $\mathbb{R}{P}^{n-1}$ spin fluid for $n=2$, 3, and 4 and $\rho {\sigma }^2=0.8$. Symbols correspond to simulated states and the curves result from the histogram reweighting technique.

Figure 3

(Color online) Size and temperature dependence of Binder’s cumulants as defined in Eq. (31) for the coplanar $\mathbb{R}{P}^{n-1}$ spin fluid for $n=2$, 3, and 4 at $\rho {\sigma }^2=0.8$. Symbols correspond to simulated states and the curves result from the histogram reweighting technique.

Figure 4

(Color online) Transition temperatures scaled with dimensionality for the coplanar $\mathbb{R}{P}^{n-1}$ spin fluid for $n=2$, 3, and 4 at $\rho {\sigma }^2=0.8$. Lines are drawn as guides to the eyes.

Figure 5

(Color online) Simulation results for the phase diagram of the planar $\mathbb{R}{P}^{n-1}$ spin fluid for $n=2$, 3, and 4. Symbols joined with dotted lines correspond to the states at which the BKT transition takes place and the line separates orientationally disordered states (lower densities) from states with quasi-long-range order (higher density, quasinematic states).